On the number of zeros of Melnikov functions
Autor: | Novikov, Dmitry, Benditkis, Sergey |
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Rok vydání: | 2010 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | We provide an effective uniform upper bond for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field. The bound depends on degrees of the field and of the perturbation, and on the order $k$ of the Melnikov function. The generic case $k=1$ was considered by Binyamini, Novikov and Yakovenko (\cite{BNY-Inf16}). The bound follows from an effective construction of the Gauss-Manin connection for iterated integrals. |
Databáze: | arXiv |
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